Gravity as Centripetal Force
Simple Explanation
For a satellite or moon orbiting a planet, there is no string and no friction — gravity alone pulls it toward the centre, and that gravitational pull is the entire centripetal force keeping it in orbit.
Why Do We Need It?
This is why astronauts on the International Space Station appear weightless: they aren't beyond gravity's reach (Earth's gravity is still very much acting on them) — they and the station are both in continuous free fall around the Earth, which feels weightless even though gravity is working exactly as it should as a centripetal force.
See It
A diagram showing a satellite on a circular orbital path with a red arrow labelled Gravity pointing inward toward the centre of the planet
Formula
Centripetal Force (from speed)
Fc = mv² / r
The net force needed to keep a mass moving on a circular path of radius r at speed v.
- Fc
- — centripetal force, in newtons (N)
- m
- — mass of the object, in kilograms (kg)
- v
- — linear (tangential) speed, in metres per second (m/s)
- r
- — radius of the circular path, in metres (m)
When to use it: Whenever you know an object's linear speed and the radius it curves around, and need the net inward force.
Worked Example
Find the centripetal force on an orbiting satellite
A 750 kg satellite orbits Earth at a speed of 7600 m/s, at an orbital radius of 6,900,000 m. Find the centripetal force gravity must supply.
Why Does This Work?
Gravity pulls every orbiting object straight toward the centre of the planet it orbits, with no sideways or outward component at all — which is exactly the direction a centripetal force must point. As long as gravity provides exactly mv²/r for the orbit's speed and radius, the object keeps circling instead of falling in or flying away.
Real-Life Example
The Moon orbiting the Earth
The Moon has been circling the Earth for billions of years without any engine or push.
Earth's gravity continuously pulls the Moon toward the centre of its orbit — precisely the centripetal force needed to keep bending the Moon's path into a (nearly) circular orbit instead of letting it drift away in a straight line.
Practice
A 500 kg satellite orbits at 8000 m/s at a radius of 8,000,000 m. What centripetal force does gravity supply? (Round to the nearest whole newton.)
MediumCommon mistake
Thinking astronauts in orbit feel weightless because they have escaped Earth's gravity — gravity at that altitude is only slightly weaker than at the surface. Weightlessness happens because the astronaut and their spacecraft are both accelerating toward Earth at exactly the same rate, in continuous free fall.
Quick Review
- For orbiting objects, gravity alone supplies the centripetal force.
- Fc = mv²/r still applies — only the source of the force changes.
- Orbiting astronauts are in continuous free fall, not beyond the reach of gravity.